I don't like to use the box which was provided for carrying my specs in. So how do I save my lenses from scratches when I am not wearing it, without using a spectacle case?
Tuck the eyeglasses in an empty pocket. The breast pocket of a shirt is ideal.
Wear the eyeglasses around your neck with eyeglasses cord/retainer. Search "eyeglasses retainer".
Keep them inside a plastic sandwich/snack bag. This will take all the scratches, and also keep the glasses from getting dusty. Of course, over time the bag will deteriorate, and you will have to replace it.
alternatively if your glasses do get scratched, you can use turtle wax to fix the minor scratches and add a layer of scratch-resistant hard wax to them.
The best way to keep from scratching is to pay attention how the glasses are laid down. They should not be laid on the lenses of course, but they should also not be laid so they flip over onto the lenses. They should not be laid so they fall on the floor. Paying attention is not as easy as it sounds and can be learned. When cleaning use only soap, warm water, and fingers. Blot with a soft cloth and do not wipe. If glasses become smudged, try and leave the smudge if not too bad until soap and water are available. Glass lenses are easier to care for, but plastic lenses require the care described, especially.